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Problem #PRU-35615

Problems Number Theory Numeral systems Decimal number system Divisibility Division with remainders. Arithmetic of remainders Division with remainder Methods Pigeonhole principle Pigeonhole principle (other)

Reception pupil Peter knows only the number 1. Prove that he can write a number divisible by 2001.

Problem #WSP-000494

Problems Number Theory Numeral systems Decimal number system Algebra Algebraic equations and systems of equations Diophantine equations

Are there any two-digit numbers which are the product of their digits?

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